Adaptive mesh refinement using piecewise-linear shape functions based on the blending function method

Use of quadrilateral elements for finite element mesh refinement can lead either to so-called 'irregular' meshes or the necessity of adjustments between finer and coarser parts of the mesh necessary. In the case of 'irregular' meshes, constraints have to be introduced in order to maintain continuity of the displacements. Introduction of finite elements based on blending function interpolation shape functions using piecewise boundary interpolation avoids these problems. This paper introduces an adaptive refinement procedure for these types of elements. The refinement is an h-method. Error estimation is performed using the Zienkiewicz-Zhu method. The refinement is controlled by a switching function representation. The method is applied to the plane stress problem. Numerical examples are given to show the efficiency of the methodology.